# Milestone to crack RSA.

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SarK0Y
Posted (edited)

Story of tails, windows and how it impacts integer factorization..
In other words, MILESTONE has been done

From the very start of my journey to discover the innards of stubborn IF, the prime goal was to have
developed binary-search-tree algos. At some point, it seemed utterly impossible. But here we go..

Actually, algo consists of three stages..

• it picks initial (probable) Z’s (pZ_L and pZ_R) up (Z = P + Q, N = P*Q). So, now algo needs to guess which one is closest to original Z.
• for pZ_L, it generates N_L which is closest to N from left/right and the same way for N_R of pZ_R.
• for N_R/L, it collects statistics of bit windows against N (their positions, widths..)..

Window(N, EntryPoint, Width) == NOT Window(N_L, EntryPoint, Width).

For instance, let Window(N, EntryPoint, Width) == “010”, then Window(N_L, EntryPoint, Width) == “101”. And now it’s possible to choose probable Z according to collected statistics for given iteration.

For tests, RSA-150 (https://en.wikipedia.org/wiki/RSA_numbers#RSA-150) has been taken, criterion to go left/right is widths of greatest windows. Output…

test mode gets activated
Wrong turn @ 1
Wrong turn @ 2
Wrong turn @ 3
Wrong turn @ 4
Wrong turn @ 5
Wrong turn @ 6
Wrong turn @ 7
Wrong turn @ 8
Wrong turn @ 9
Wrong turn @ 10
Wrong turn @ 11
Wrong turn @ 12
Wrong turn @ 13
Wrong turn @ 14
Wrong turn @ 15
Wrong turn @ 16
Wrong turn @ 17
Wrong turn @ 18
Wrong turn @ 19
Wrong turn @ 20
Wrong turn @ 21
Wrong turn @ 22
Wrong turn @ 23
Wrong turn @ 24
Wrong turn @ 25
Wrong turn @ 26
Wrong turn @ 27
Wrong turn @ 28
Wrong turn @ 29
Wrong turn @ 30
Wrong turn @ 31
Wrong turn @ 32
Wrong turn @ 33
Wrong turn @ 34
Wrong turn @ 35
Wrong turn @ 36
Wrong turn @ 37
Wrong turn @ 38
Wrong turn @ 39
Wrong turn @ 40
Wrong turns == 40

nice turns == 208
Total iterations == 248

In short, algo doesn’t do gaps (good and bad turns ain’t shuffled/mixed) even with such rather primitive criterion.
Archive: https://sourceforge.net/projects/fastprimecruncher/

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